A Fourier transform spectroscopy method (a Fourier transform frequency analysis method) is a spectroscopic technique where spectra are obtained by measuring a temporal waveform or interferogram of electromagnetic radiation, or other types of radiation, and calculating its Fourier transform.
When a periodical signal is considered, a temporal waveform signal h(t) observed in a time domain is related with a frequency spectrum H(f) observed in a frequency domain based on the Fourier transform (Equation (1)) and the inverse Fourier transform (Equation (2)) as are shown by the following Equations.
[Equation 1]H(f)=∫−∞∞h(t)exp(−2πift)dt  (1)[Equation 2]h(t)=∫−∞∞H(f)exp(2πift)df  (2)
Signals in a time domain and in a frequency domain are considered to be equivalent to each other from the relations of the Fourier transform and the inverse Fourier transform. Before computers became available, measurements in a frequency (or wavelength) domain were generally performed for the spectrum measurement due to a difficulty in performing the Fourier transform.
For example, in optical spectroscopy such as dispersive spectrometers, a spectrum was acquired by spatially separating multiple wavelength components of light with dispersive optical elements (a diffraction grating, a prism and so on) and selecting only a specific wavelength component.
However, the Fourier transform became extremely easy as computers became available, which made it possible to acquire the spectrum for each frequency by the Fourier transform of a measured temporal waveform of a phenomenon, namely, the Fourier transform spectroscopy.
Typical examples of the Fourier transform spectroscopy method includes a pulse Fourier-transform nuclear magnetic resonance spectroscopy method (FT-NMR), a nuclear magnetic resonance imaging method (MRI), a Fourier-transform infrared spectroscopy method (FT-IR), a terahertz time-domain spectroscopy method (THz-TDS) and so on, and these are widely used in industrial fields and medical fields. A FT-NMR irradiates pulsed high frequency radio waves (radio waves) on a sample tube set at the center of a superconducting magnet and measures a time domain signal called FID (Free Induction Decay) and consequently a NMR spectrum is acquired by the Fourier transform of this FID. A Nuclear Magnetic Resonance Imaging (MRI) applies NMR spectra to computed tomography. A FT-IR and a THz-TDS observe interferogram and electric field as a function of time, respectively, and spectra are acquired after the Fourier transform of them.                Features of a Fourier transform spectroscopy method are includes the following 1) to 4).        
1) High Signal Intensity.                The signal intensity is high and hence a high signal-to-noise ratio is acquired because the whole spectral components of input signal is collected at the same time by acquiring the time-domain signal in the Fourier transform spectroscopy method.        
2) Bright Optical System without Slits.                High optical throughput and a high signal-to-noise ratio can be realized because slits required in a dispersive spectrometer are not necessary and its optical system is brighter than that of dispersive spectrometer.        
3) A Continuous Spectrum with High Spectral Accuracy.
Continuous spectrum can be observed and its spectral accuracy is relatively high due to Fourier transform.
4) Applicable to Various Electromagnetic Regions.
The Fourier transform spectroscopy method is now becoming the main stream of the spectroscopic measurement and is now widely used in various fields thanks to the features mentioned above.
TABLE 1Fourier transform spectroscopy methodApplication fieldNuclear magnetic resonance Structural determination of organicspectroscopy method (NMR)substances and so onNuclear magnetic resonance imagingBiological body tomography imaging and, so onFourier transform infrared spectroscopySemiconductor defect Drug and inspection method (FT-IR)food analysis and so onTerahertz time domain spectroscopy Drug analysis, Non-destructive method (THz-TDS)inspection Protein identificationFourier transfer mass spectroscopy Protein identificationmethod (FT-MS)Fourier transfer optical spectrum Optical communication, optical analyzerdevice evaluationFourier transform spectrum analyzerElectronic device evaluation
The important characteristics of the spectroscopy are the spectral resolution and the spectral accuracy.
FIG. 1 shows a temporal waveform of an observed signal and the corresponding amplitude spectrum obtained by its Fourier transform. When the temporal waveform of a phenomenon is measured, the spectral resolution is simply determined by the inverse of the measurement time window size during which the temporal waveform is observed (an observation time window). Therefore, as the time window is increased, the spectral resolution is enhanced. On the other hand, when the phenomenon repeats, it is generally accepted that the achievable spectral resolution is limited to its repetition frequency (theoretical limit of spectral resolution) because the maximum window size is restricted to a single repetition period to avoid the coexistence of multiple signals. Also, when the majority of the signal components are temporally localized, excessive extension of the window size increases the noise contribution.
Also, the acquisition time increases in proportion to the expansion of the observation time window size. Furthermore, in the case of optical FTS, the travel range of a translation stage used for time-delay scanning practically limits the spectral resolution. The practical spectral resolution is far lower than the spectral resolution to be determined by the repetition frequency and it is not easy to realize a sufficiently large size of the observation time window. Considering such these factors, the actual observation time window size is selected, which determines the spectral resolution.
On the other hand, the spectral accuracy depends on the accuracy of time sampling in the temporal waveform.
For improving the substance identification capacity in spectroscopic analysis, further improvement of the spectral resolution and the spectral accuracy are necessary.
Some inventors among the inventors of this invention have already proposed a measurement equipment of a high speed THz spectrometry with a spectral resolution of a theoretical limit (=repetition frequency=mode-locked frequency) in the THz-TDS. (Refer to Patent Literature 1)
The present invention resolves a limitation of spectral resolution in the Fourier transform spectroscopy including the THz-TDS, realizes a theoretically infinitesimal spectral resolution (an infinite spectral resolving power) and improves a spectral accuracy remarkably.